Penalized Regression Splines in Mixture Density Networks

Abstract Mixture Density Networks (MDN) belong to a class of models that can be applied to data which cannot be sufficiently described by a single distribution since it originates from different components of the main unit and therefore needs to be described by a mixture of densities. In some situations, however, MDNs seem to have problems with the proper identification of the latent components. While these identification issues can to some extent be contained by using custom initialization strategies for the network weights, this solution is still less than ideal since it involves subjective opinions. We therefore suggest replacing the hidden layers between the model input and the output parameter vector of MDNs and estimating the respective distributional parameters with penalized cubic regression splines. Applying this approach to data from Gaussian mixture distributions as well gamma mixture distributions proved to be successful with the identification issues not playing a role anymore and the splines reliably converging to the true parameter values.